It's Tuesday night at the Green Mill, and the artists who have created this remarkable scene – they call themselves the Fat Babies – appear to be having about as much fun as the Chicagoans they're entertaining. Better still, they're playing music from the dawn of the Jazz Age with an exuberance and stylistic authenticity infrequently encountered these days, and certainly not very often from instrumentalists mostly in their 20s and 30s.

Close your eyes, and you'd think the calendar had flipped back nearly a century, when both the Green Mill and the music were new and Chicago itself was emerging as a jazz nexus.

"My goal is to play this music they way it should be," 31-year-old bandleader-bassist Beau Sample tells a visitor, before launching the evening's first set.

A former Texan who migrated to Chicago from Austin in 2007 to play an early-period jazz widely identified with this city, Sample speaks with the fervency of a jazz missionary.

"We want to play this music not as a caricature," he adds, "and not as a museum piece."

Those, of course, are the two extremes to which vintage jazz typically is subjected: either as musical exaggeration or as fussy academic exercise.

The Fat Babies find the sweet spot between those two extremes, giving the music plenty of tonal muscle and rhythmic verve but also recapturing the stylistic idiosyncrasies of the period: whooping phrases, sleek glissandos, buoyant dance rhythms.

The band documented this work on its debut album, "Chicago Hot" (Delmark Records), one of the best jazz releases of 2012, the recording proof positive that this music still can feel alive and contemporary – yet also true to the performance practices of the era. Beautifully recorded, "Chicago Hot" illuminated how this music might have sounded if musicians of the Roaring 20s had benefited from today's lucid recording technology.

Purists might quibble with the Fat Babies' use of stand-up bass rather than tuba, but perhaps that small concession to contemporary expectations helps catapult these ancient scores into the 21st century (and even Morton and Armstrong featured bass in some of their early-period work).

"I think tuba was more prominent in jazz bands of the '20s (outside of New Orleans), but it does not bother me to do a song that was originally recorded with tuba and play it with string bass," explains Sample in an email.

"It would be very limiting to only play songs that had our specific instrumentation on the original records. I am trying to achieve authenticity in the spirit of the music first and foremost. That's my goal, and that's what I want to come across. I really think it's most authentic when it has an authentic energy behind the performance."

Which leads to why this band calls itself the Fat Babies. The term, says Sample, goes back generations where he grew up, as in: "That's hotter than a fat baby."

On this evening, these Fat Babies are scalding, but not in ways that you might expect: Not with overheated tempos or frantic solos. Instead, the band plays this music with plenty of energy and zest, yet not so fast that the dancers can't keep up.

The Babies open their set with "San," their bright tone, taut rhythms and exuberant manner instantly drawing young dancers – and older ones – to the tiny spot in front of the bandstand where tables have been cleared. In "Dardanella," John Otto's tender solo on alto saxophone and Paul Asaro's ebullient stride-piano technique vividly evokes an earlier era.

If Sample is the visionary-leader of the project, cornetist Andy Schumm is its melodic heart, his lyric phrases and glistening ensemble arrangements establishing the sonic framework for the band. Schumm's radiant cornet solo on "Our Bungalow of Dreams" reiterates the poetry of the venture. All the while, the chugging rhythm section – powered by Jake Sanders' banjo, Asaro's James P. Johnson-like piano accompaniment and Sample's surging bass lines – keeps the dancers in nearly perpetual motion.

Though it's true that, in concert, the band doesn't achieve quite the technical acuity and instrumental balances they attained on the recording, their work certainly is strong enough for the occasion. And when cornetist Schumm, reedist Otto and trombonist Dave Bock stand up to play the rousing finale of the set, in "Shaking the Blues Away," the theatricality of the gesture inspires spontaneous applause. Who wouldn't be moved by the sight and sound of this?

You don't encounter pre-bebop jazz of this quality and commitment very often anymore. And while Sample and the Fat Babies hasten to note the debt they owe to the Salty Dogs, a long-running vintage-jazz band, the heirs apparent clearly bring a fresh perspective to the early repertoire.

Thanks to the Fat Babies, trad jazz still plays hard in Chicago, the town that imported this music from New Orleans and nurtured it, perfected it and sent it around the world.

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